Is there a Relationship between the nozzle size and the diameter of the filament?

For example: ''Lulzbot support'' told me that for nozzle that are smaller, it is better to use 1,75mm filament.To me, it makes no sense. The threaded rod size is what we have to look to know what filament diameter we should use. Not the nozzle size.

yes and no, there is a relationship between nozzle size and layer height. I believe rule of thumb is no more than 75% ie .4 nozzle = max .3mm layer height. I believe this is what you were referring to. Filament diameter is completely different and is determined by extruder more than nozzle size if that makes sense. If you wanted a 1.2mm nozzle then 3mm filament would allow you to print faster at higher layer heights as you would need more material delivered faster. for most printing around .2 or .3 i don't think it matters as you are limited by print speed before hitting extrude limits. I am sure my betters will correct me if i am wrong on this...

seems logical. lulzbot (print your mind 3d) told me that the extruder is made for 2.85cm filament. Hé said that it can work with 1.75cm filament but not that well... and that is better to work with 2.85cm filament.

That statement is true. I think you are getting confused between "extruder" and "nozzle".

The extruder is the mechanism that pushes the filament to the nozzle. Most extruders pinch the filament to gain traction to allow it to push. What Lulzbot is telling you is that the extruder is designed to grab onto 2.85mm (3mm) filament but CAN grip onto 1.75mm but not as well. This has nothing to do with nozzle size.

Now, speaking of nozzle size, smaller nozzles DO work better with smaller diameter filament. What is better is resolution which equates to better control of how much plastic is being extruded at any given point in the printing process. During one step of the extruder stepper, more plastic will be extruded using 3mm filament then with 1.75mm. Therefor, extruder resolution will be much higher using the 1.75mm over the 3mm. When using larger nozzles, this does not have as much of an effect as much more plastic is being requested at a time causing the need for more steps to be used negating the need for the higher resolution.

May I add that smaller diameter filament can be heated through to its core more quickly than larger diameter filament (less distance for the heat to travel from surface to core).

That would result in a lower internal pressure at the tip, and in turn to less thrust required from the extruder gear.But conversely a larger tip orifice diameter would also result in a lower internal pressure.

So for very small diameter tips, a smaller filament diameter (with all the other components in the chain suitably sized for the smaller filament as well) may indeed work better.